The Alternatives 1 and 2 in the Following Payoff Table $\text { States of nature }$

question 24

Essay

The alternatives 1 and 2 in the following payoff table represent the two possible manufacturing strategies that the EKA manufacturing company can adopt.The level of demand affects the success of both strategies.The states of nature (S_i,i = 1,2 3)represent the levels of demand for the company products.S₁,S₂,and S₃ characterize high,medium,and low demand respectively.The payoff values are in thousands of dollars. $\text { States of nature }$
$\begin{array} { | l | r | r | r | } \hline \text { Alternatives } & \mathbf { s } _ { \mathbf { 1 } } & \mathbf { s } _ { \mathbf { 2 } } & { \mathbf { s } _ { \mathbf { 3 } } } \\\hline \text { Strategy 1 } & 110 & 80 & 70 \\\hline \text { Strategy 2 } & 60 & 120 & 50 \\\hline\end{array}$ The management believes that the weather conditions significantly affect the level of demand.48 monthly sales reports are randomly selected.These monthly sales reports showed 15 months with high demand,28 months with medium demand,and 5 months with low demand.12 of the 15 months with high demand had favourable weather conditions.14 of the 28 months with medium demand had favourable weather conditions.Only 1 of the 5 months with low demand had favourable weather conditions.Based on this information,the prior probabilities have been revised.If the weather conditions are favourable,P(S₁)= .4286,P(S₂)= .5357,and P(S₃)= .0357,and if the weather conditions are poor,P(S₁)= .1364,P(S₂)= .6818,and P(S₃)= .1818.It is also determined that the probability of favourable weather is 0.56 and the probability of poor weather is 0.44.
-Carry out a preposterior analysis and using the revised probabilities,determine the expected monetary value when the weather conditions are favourable and determine the expected monetary value when the weather conditions are poor.

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